![]() The trick by example: flipping edgesIt's no mystery what is tricky about solving a Cube beyond the first layer: just about anything you try next will destroy parts of the layer that you've just painstakingly sorted out. However, to understand how the trick works in principle, there are no prerequisites. To repeat, to actually be able to apply the trick I am about to describe you have to be comfortable solving the first layer. By "solving the first layer" I mean twisting the Cube until all the nine pieces with stickers of one color are arranged exactly as in a solved Cube. To make sure we're all on the same page, let's start by stating the (almost) obvious. You'll still need to do some work to put the trick into practice: perhaps about the same amount of work as it took to figure out how that first layer of the Cube works. However, actually finding a solution to the Cube does not come for free. I’d like to stress that the purpose of this article is to give you a good chance of "doing it all by yourself", any time you choose and with no help from others. It seems more that the trick tends to get lost in the fiddly details of particular solutions. And it's not that these experts are attempting to protect a treasured trade secret. ![]() It's well-known and used by many genuine twisty puzzle solvers. This probably all sounds too good to be true, but the trick is easy to learn and it really works. And, even if you haven't yet solved that first layer, you'll be able to understand how the trick works and will be able to remember and apply it: ideal for the next time you're stranded on a desert island with only a Rubik's Cube to keep you occupied. Provided you know how to solve the first layer, this trick will allow you to derive your very own recipes for solving the Cube, and for many other twisty puzzles. What I want to do here is to share with you a simple but very powerful trick. Moreover, you've possibly now forgotten almost everything about that recipe, leaving you with little chance of unscrambling the next Cube that confronts you. But, of course, this really is "solving", not solving, and it's not nearly as satisfying as the real thing. You may then have gone on to "solve" the Cube by following one of the ready-made recipes available in books and on the internet. If so then you're in the good company of millions of others. How far did you get? Could you figure out the whole thing? Or did you just manage to fix one layer, but then were not able to progress any further? You’re a mathematician, so chances are that at some point you've played around with Rubik’s Cube. And, on its return, the Cube has been accompanied by hundreds of related twisty puzzles demanding to be unscrambled. There have also been some exciting new developments, such as complex solving methods, new Cube designs and streamlined ways of manipulating the Cube that allow experts to solve the Cube in under 10 seconds. Rubik’s Cube is back! After years of relative quiet it is once again common to see people twisting away at their Cubes. This is an extended version of an article that appeared in the April 2013 issue of Math Horizons. Write Your Own Recipe for Rubik’s Cube Burkard Polster
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